Internal problem ID [15140]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 12. Miscellaneous problems. Exercises page 93
Problem number: 278.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _exact, _rational, _dAlembert]
\[ \boxed {-3 y^{2} x +\left (y^{3}-3 y x^{2}\right ) y^{\prime }=-x^{3}} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 119
dsolve((x^3-3*x*y(x)^2)+(y(x)^3-3*x^2*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {\sqrt {3 c_{1} x^{2}-\sqrt {8 c_{1}^{2} x^{4}+1}}}{\sqrt {c_{1}}} \\ y \left (x \right ) &= \frac {\sqrt {3 c_{1} x^{2}+\sqrt {8 c_{1}^{2} x^{4}+1}}}{\sqrt {c_{1}}} \\ y \left (x \right ) &= -\frac {\sqrt {3 c_{1} x^{2}-\sqrt {8 c_{1}^{2} x^{4}+1}}}{\sqrt {c_{1}}} \\ y \left (x \right ) &= -\frac {\sqrt {3 c_{1} x^{2}+\sqrt {8 c_{1}^{2} x^{4}+1}}}{\sqrt {c_{1}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 7.89 (sec). Leaf size: 245
DSolve[(x^3-3*x*y[x]^2)+(y[x]^3-3*x^2*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {3 x^2-\sqrt {8 x^4+e^{4 c_1}}} \\ y(x)\to \sqrt {3 x^2-\sqrt {8 x^4+e^{4 c_1}}} \\ y(x)\to -\sqrt {3 x^2+\sqrt {8 x^4+e^{4 c_1}}} \\ y(x)\to \sqrt {3 x^2+\sqrt {8 x^4+e^{4 c_1}}} \\ y(x)\to -\sqrt {3 x^2-2 \sqrt {2} \sqrt {x^4}} \\ y(x)\to \sqrt {3 x^2-2 \sqrt {2} \sqrt {x^4}} \\ y(x)\to -\sqrt {2 \sqrt {2} \sqrt {x^4}+3 x^2} \\ y(x)\to \sqrt {2 \sqrt {2} \sqrt {x^4}+3 x^2} \\ \end{align*}